The paper proposes the extensions of the available linear and cubic interpolation methods for backprojecting complex SAR data into an image plane. Due to the fact that the phase of complex SAR data is very sensitive to the shift in time, the proposed interpolations include the phase control of the interpolated complex values. The proposed methods are examined with the global backprojection algorithm that is used to process SAR data at THz frequencies. In numerical examples, a two-dimensional indoor THz SAR imaging for a point target is considered, where the developed interpolation methods are compared with the nearest neighbor approach. © 2021 IEEE.